Let f(x,y)=e^(−5x)sin(3y).
(a) Using difference quotients with Δx=0.1 and Δy=0.1, we
estimate
fx(3,2)≈
fy(3,2)≈
(b) Using...
Let f(x,y)=e^(−5x)sin(3y).
(a) Using difference quotients with Δx=0.1 and Δy=0.1, we
estimate
fx(3,2)≈
fy(3,2)≈
(b) Using difference quotients with Δx=0.01 and Δy=0.01, we find
better estimates:
fx(3,2)≈
fy(3,2)≈
5. Let v1 = (1/3,−2/3,2/3), v2 = (2/3,−1/3,−2/3) and v3 =
(2/3,2/3,1/3).
(a) Verify that v1,...
5. Let v1 = (1/3,−2/3,2/3), v2 = (2/3,−1/3,−2/3) and v3 =
(2/3,2/3,1/3).
(a) Verify that v1, v2, v3 is an orthonormal basis of R 3 .
(b) Determine the coordinates of x = (9, 10, 11), v1 − 4v2 and
v3 with respect to v1, v2, v3.
For the data set
(−2,−1),(3,2),(6,5),(8,8),(11,11),(−2,−1),(3,2),(6,5),(8,8),(11,11),
carry out the hypothesis test
H0H1β1=0β1≠0H0β1=0H1β1≠0
Determine the value of the...
For the data set
(−2,−1),(3,2),(6,5),(8,8),(11,11),(−2,−1),(3,2),(6,5),(8,8),(11,11),
carry out the hypothesis test
H0H1β1=0β1≠0H0β1=0H1β1≠0
Determine the value of the test statistic and the associated
p-value.
Test Statistic =
p-Value =
X1,...,X81 ⇠ N(0,1) and Y1,...,Y81 ⇠ N(3,2 ). For each
i, Corr(Xi,Yi)= 1/2. Let Zi =...
X1,...,X81 ⇠ N(0,1) and Y1,...,Y81 ⇠ N(3,2 ). For each
i, Corr(Xi,Yi)= 1/2. Let Zi = Xi + Yi.
1. Compute Var(Zi).
2. Approximate P [ Zi > 243]. (Explain your answer.)